Issai Schur (10 January 1875 – 10 January 1941) was a Russian mathematician who worked in Germany for most of his life. He studied at the University of Berlin. He obtained his doctorate in 1901, became lecturer in 1903 and, after a stay at the University of Bonn, professor in 1919.
As a student of Ferdinand Georg Frobenius, he worked on group representations (the subject with which he is most closely associated), but also in combinatorics and number theory and even theoretical physics. He is perhaps best known today for his result on the existence of the Schur decomposition and for his work on group representations (Schur's lemma).
Schur published under the name of both I. Schur, and J. Schur, the latter especially in Journal für die reine und angewandte Mathematik. This has led to some confusion.
Issai Schur was born into a Jewish family, the son of the businessman Moses Schur and his wife Golde Schur (née Landau). He was born in Mogilev on the Dnieper River in what was then the Russian Empire. Schur used the name Schaia (Isaiah as the epitaph on his grave) rather than Issai up in his middle twenties. Schur's father may have been a wholesale merchant.
In 1888, at the age of 13, Schur went to Liepāja (Courland, now in Latvia), where his married sister and his brother lived, 640 km north-west of Mogilev. Courland was one of the three Baltic governorates of Tsarist Russia, and since the Middle Ages the Baltic Germans were the upper social class. The local Jewish community spoke mostly German and not Yiddish.
Schur attended the German-speaking Nicolai Gymnasium in Libau from 1888 to 1894 and reached the top grade in his final examination, and received a gold medal. Here he became fluent in German.
In October 1894, Schur attended the University of Berlin, with concentration in mathematics and physics. In 1901, he graduated summa cum laude under Frobenius and Lazarus Immanuel Fuchs with his dissertation On a class of matrices that can be assigned to a given matrix, which contains a general theory of the representation of linear groups. According to Vogt, he began to use the name Issai at this time. Schur thought that his chance of success in the Russian Empire was rather poor, and because he spoke German so perfectly, he remained in Berlin. He graduated in 1903 and was a lecturer at the University of Berlin. Schur held a position as professor at the Berlin University for the ten years from 1903 to 1913.
In 1913 he accepted an appointment as associate professor and successor of Felix Hausdorff at the University of Bonn. In the following years Frobenius tried various ways to get Schur back to Berlin. Among other things, Schur's name was mentioned in a letter dated 27 June 1913 from Frobenius to Robert Gnehm (the School Board President of the ETH) as a possible successor to Carl Friedrich Geiser. Frobenius complained that they had never followed his advice before and then said: "That is why I can't even recommend Prof. J. Schur (now in Bonn) to you. He's too good for Zurich, and should be my successor in Berlin". Hermann Weyl got the job in Zurich. The efforts of Frobenius were finally successful in 1916, when Schur succeeded Johannes Knoblauch as adjunct professor. Frobenius died a year later, on 3 August 1917. Schur and Carathéodory were both named as the frontrunners for his successor. But they chose Constantin Carathéodory in the end. In 1919 Schur finally received a personal professorship, and in 1921 he took over the chair of the retired Friedrich Hermann Schottky. In 1922, he was also added to the Prussian Academy of Sciences.
After the takeover by the Nazis and the elimination of the parliamentary opposition, the Law for the Restoration of the Professional Civil Service on 7 April 1933, prescribed the release of all distinguished public servants that held unpopular political opinions or who were "Jewish" in origin; a subsequent regulation extended this to professors and therefore also to Schur. Schur was suspended and excluded from the university system. His colleague Erhard Schmidt fought for his reinstatement, and since Schur had been a Prussian official before the First World War, he was allowed to participate in certain special lectures on teaching in the winter semester of 1933/1934 again. Schur withdrew his application for leave from the Science Minister and passed up the offer of a visiting professorship at the University of Wisconsin–Madison for the academic year 1933–34. One element that likely played a role in the rejection of the offer was that Schur no longer felt he could cope with the requirements that would have come with a new beginning in an English-speaking environment.
Already in 1932, Schur's daughter Hilde had married the doctor Chaim Abelin in Bern. As a result, Issai Schur visited his daughter in Bern several times. In Zurich he met often with George Pólya, with whom he was on friendly terms since before the First World War.
On such a trip to Switzerland in the summer of 1935, a letter reached Schur from Ludwig Bieberbach signed on behalf of the Rector's, stating that Schur should urgently seek him out in the University of Berlin. They needed to discuss an important matter with him. It involved Schur's dismissal on 30 September 1935.
Schur remained a member of the Prussian Academy of Sciences after his release as a professor, but a little later he lost this last remnant of his official position. Due to an intervention from Bieberbach in the spring of 1938 he was forced to explain his resignation from the commission of the Academy. His membership in the Advisory Board of Mathematische Zeitschrift was ended in early 1939.
Schur found himself lonely after the flight of many of his students and the expulsion of renowned scientists from his previous place of work. Only Dr. Helmut Grunsky had been friendly to him, as Schur reported in the late thirties to his expatriate student Max Menachem Schiffer. The Gestapo was everywhere. Since Schur had announced to his wife his intentions to commit suicide in case of a summons to the Gestapo, in the summer of 1938 his wife took his letters, and with them a summons from the Gestapo, sent Issai Schur to a relaxing stay in a home outside of Berlin and went with medical certificate allowing her to meet the Gestapo in place of her husband. There they flatly asked why they were still staying in Germany. But there were economic obstacles to the planned emigration: emigrating Germans had a pre-departure Reich Flight Tax to pay, which was a quarter of their assets. Now Schur's wife had inherited a mortgage on a house in Lithuania, which because of the Lithuanian foreign exchange determination could not be repaid. On the other hand, Schur was forbidden to default or leave the mortgage to the German Reich. Thus the Schurs lacked cash and cash equivalents. Finally, the missing sum of money was somehow supplied, and to this day it does not seem to be clear who were the donors.
Schur was able to leave Germany in early 1939. His health, however, was already severely compromised. He traveled in the company of a nurse to his daughter in Bern, where his wife also followed a few days later. There they remained for several weeks and then emigrated to Palestine. Two years later, on his 66th birthday, on 10 January 1941, he died in Tel Aviv of a heart attack.
Schur continued the work of his teacher Frobenius with many important works for group theory and representation theory. In addition, he published important results and elegant proofs of known results in almost all branches of classical algebra and number theory. His collected works are proof of this. There, his work on the theory of integral equations and infinite series can be found.
In his doctoral thesis Über eine Klasse von Matrizen, die sich einer gegebenen Matrix zuordnen lassen Issai Schur determined the polynomial representations of the general linear group
{\displaystyle GL(n,\mathbb {C} )}
of complex numbers. The results and methods of this work are still relevant today. In his book, J.A. Green determined the polynomial representations of